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a(n) = mu(A327859(n)), where mu is the Möbius function, A008683.
5

%I #6 Feb 28 2021 20:28:24

%S 1,1,-1,-1,0,-1,0,-1,0,-1,1,-1,0,-1,-1,1,1,-1,0,-1,0,0,0,-1,0,0,0,0,1,

%T -1,1,-1,0,0,0,0,0,-1,0,0,0,-1,0,-1,0,1,0,-1,0,0,0,0,0,-1,0,0,0,0,1,

%U -1,0,-1,-1,0,0,0,0,-1,0,0,0,-1,0,-1,1,0,0,0,0,-1,0,0,0,-1,0,0,0,1,0,-1,0,0,0,0,0,0,0,-1,0,0,0,-1,0,-1,0,0

%N a(n) = mu(A327859(n)), where mu is the Möbius function, A008683.

%H Antti Karttunen, <a href="/A341517/b341517.txt">Table of n, a(n) for n = 0..65537</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%F a(n) = A008683(A327859(n)) = A008683(A276086(A003415(n))).

%F For all n > 1, abs(a(n)) = [A328390(n)==1], where [ ] is the Iverson bracket.

%F a(p) = -1 for all primes p.

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o A327859(n) = A276086(A003415(n));

%o A341517(n) = moebius(A327859(n));

%Y Cf. A003415, A008683, A276086, A327859, A328390.

%Y Absolute values give the characteristic function sequence for A341518.

%K sign

%O 0

%A _Antti Karttunen_, Feb 28 2021